where \(\mathbb {E}^k_{\text{signal}}(\mathbf {\Theta })\)  = \(\mathbb {E}\big \lbrace ||\textbf {g}_k||^4\big \rbrace \) , \(\mathbb {E}^k_{\text{noise}}(\mathbf {\Theta })\)  = \(\mathbb {E}\big \lbrace ||\textbf {g}_k||^2\big \rbrace \) , \(\mathbb {E}^k_{\text{interf}}(\mathbf {\Theta }) = \mathbb {E}\big \lbrace |\textbf {g}_k^H\textbf {g}_i|^2\big \rbrace  \) . \(\mathbb {E}_{\text{signal}}^k(\mathbf {\Theta })\) , \(\mathbb {E}_{\text{interf}}^k(\mathbf {\Theta })\) , \(\mathbb {E}_{\text{noise}}^k(\mathbf {\Theta })\)  and \(\mathbb {E}_{\text{hwi}}^k(\mathbf {\Theta }) \)  are respectivly given by (REF ), (REF ), (REF ) and (REF ). The derivations of the first three terms can be found in [1]} and the fourth term is proved in Appendix A. Besides, \(a_k\overset{\Delta }{=}\frac{\nu \mu _k}{(\rho +1)(\epsilon _k+1)}\) , \(\text{g}_{k_m} \) is the \(m\) -th element of \(\textbf {g}_k\) , \(f_k(\mathbf {X})\overset{\Delta }{=}\textbf {a}_N^H(\phi ^a_{rb},\phi ^e_{rb})\mathbf {X}\overline{\textbf {h}}_k\) .
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